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- เผยแพร่เมื่อ 6 ก.พ. 2025
- 2016 AP Calculus BC Exam Free Response Question #6
The Series question! Write four nonzero terms of a Taylor polynomial and the general term. Determine convergence at the end points of the interval of convergence given the center and the radius. Approximate a value using a Taylor polynomial. Alternating Series error term.
This is a great video! It doesn't go super slow, gets to all the facts, and is very clear through every step of the process. Thank you! I'm definitely subbing, and I will continue to watch these videos even after the AP Test!
Thank you so much, the calc exam is tomorrow and this is incredibly helpful!!!
Last minute study gang
Good luck tho
SUCH A GOOD VIDEO!
Thank you!
THANK YOU SO SO MUCH
Very Helpful
Glad to help! Please share with anyone you think will benefit!
How did you simplify the general term in part a
Wondering about this too
n! can also equal n(n-1)! which allows you to cancel out the (n-1)!'s I believe@@asknorway
this may seem like an obvious question, but could you just leave the derivative terms (i.e. f'' and f''') in unsimplified form and write out the terms of the series using those expanded forms rather than using 1/4 and -1/4? I understand that it's not very important here, but in other cases when simplifying would be time consuming, could you do that?
That's a really good question. Yes, you can leave it unsimplified. Get down to numerical values and then just leave it and move on.
I don't do that most of the time because it makes me vaguely uncomfortable to see unsimplified things in a final answer but the AP exam is totally fine with it.
do they teach this onlyu at the university or do they show it in grade 12 AP Calculus
This is an actual question that was on the ap calc bc exam in 2016, so definitely in 12th grade (or even 10th or 11th, depending on when you get there)
@@turksvids thx for the info { if you understand well how algebra work is it gonna help some say it's easier then regular algebra like I said before thanks for your support
If you understand algebra very well it will make Calc BC much easier. There are some topics in Calc BC that are much harder than things you see in Algebra, though. I'd say a really good understanding of Algebra and Trigonometry is a good background for calculus.
Where did the addition of a 1 come into the equation for part b?
I wrote a summation for the series but the summation only started working after the first term, so the 1 that's hanging out there is actually the 0th term of the series, but it doesn't fit the pattern of the nth term that I put in the summation. Adding or subtracting a number from a series doesn't change the convergence of the series, though, so it doesn't impact checking the end points of the interval of convergence. Hope this helps!
@@turksvids It did! Thank you so much!! I don't how I would review these FRQs without your videos
Thanks
in b, why don't we use the ratio test as we did in 2018 bc?
hi! we didn't need to use the ratio test to find the radius of convergence in this case because it was given in the problem. Since we knew the center and we knew the radius, all we really needed to do was check the end points for this problem. From the given information the series was guaranteed to converge from -1
@@turksvids that is bit hard
Do general terms always start at n=0 or n=1? Please help!
No, they can start at anything. My advice would be unless you specifically need to write a summation you should just write the first however many terms they ask for, put a + ... +, and then the general term. I don't mess with summations unless I have to.
Watch out for geometric series that start their summation at a number other than zero! If a geometric series converges its sum is (the first term wherever it comes from)/(1 - ratio).
turksvids How would the test graders know what I intended to start with? Also, do you have any tips for writing general terms?